Even if you believe every group has a different coefficient, I would also
estimate the pooled model and use interactions to test whether the
coefficients really are different across groups. If you only estimate
separate models for each group, you are unable to test the assumption
(unless you simply eyeball coefficients and make an ad hoc decision).
There are some other issues to consider (e.g., is it appropriate to assume
the same error structure for the different groups?) but the pooled model
seems a place to start, at least in my area of research and perhaps in
yours as well.
Hope this helps.
Sam
A variation on that concern: You'll occasionally see statements like "The
effect of education is significant for whites but not for blacks" - which
is true but when you look at the actual coefficients they are very similar
for the 2 groups. They probably don't significantly differ from each
other; the fact that the coefficient is significant in one group but not
the other probably just reflects differences in sample size. When doing
group comparisons, just looking at whether coefficients within each group
are statistically significant can be very misleading if you then use that
as a basis for making group comparisons. As Sam says, you should do formal
tests of the group differences.
